Geometry of Complex Numbers: Difference between revisions

Revision as of 12:13, 31 March 2023

Revision as of 12:05, 8 November 2023

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==Topics==

The book is divided into three chapters, corresponding to the three parts of its subtitle: circle geometry, [[Möbius transformation]]s, and non-Euclidean geometry. Each of these is further divided into sections (which in other books would be called chapters) and sub-sections. An underlying theme of the book is the representation of the [[Euclidean plane]] as the [[Complex plane|plane of complex number]]s, and the use of [[complex numbersnumber]]s as coordinates to describe geometric objects and their transformations.{{r|hunacek}}

The chapter on circles covers the [[analytic geometry]] of circles in the complex plane.{{r|monk}} It describes the representation of circles by <math>2\times 2</math> [[Hermitian matrix|Hermitian matrices]],{{r|goodman|crowe}} the [[Inversive geometry|inversion of circles]], [[stereographic projection]], [[Apollonian circles|pencils of circles]] (certain one-parameter families of circles) and their two-parameter analogue, bundles of circles, and the [[cross-ratio]] of four complex numbers.{{r|goodman}}